3 ft. from the same point. What lifting-force will be exerted on the plunger, and what will be the pressure on the pin by a downward thrust of 20 lb. at the hand; this being just force enough to work the pump?

13. The arms of a balance are x and y. When a mass w is placed in one scale-pan, 16 lb. placed in the other pan will just balance it. When the mass, w, is placed in the other pan, only 9 lb. are needed to balance it. What is the correct weight of w? What are the lengths of the arms?

Solution: Law II gives (-w)(-x)+(+F) (0)+(-16)(+6) =0, or wx=16y, for the first weighing; Law II gives (−9) (−x) + (+F)(0)+(+w)(+y)=0, or 9x=wy, for the second weighing.

Dividing, we readily find w=1144=±12. Interpret the double sign. Here algebra shows itself liberal and provides for the possibility that the weights may pull either upward or downward. Taking other values instead of the 9 and 16, as 10 and 12, we have a practical problem for the introduction to the study of radicals, for we should then have w±√120

=

Multiplying the equations, we readily find

土

Interpret. Can the plus sign have meaning here? If

x

y

10 lb. and 12 lb. were used, we should have 1/19, and again there is a call for radicals.

Common road wagons, carriages, automobiles, floor-joists, bridge-girders, roof-trusses, etc., furnish an abundance of conditions calling for simultaneous equations. The reply that such problems call for much technical knowledge is untenable. Only the two laws already given are needed.. Space permits only a few more examples to illustrate how this work may be given a formal turn. 14. A floor-joist lies at rest under the three parallel forces +x, +y, and 5, whose arms are, +3, −2, and +1, respectively. Find the strength of the unknown forces x and y.

15. A bridge-girder is at rest under the action of the forces +x, — 10, +y, and 2, with arms, respectively, −4, +2, +5, and +11. Find x

and y.

When quadratics are wanted, such problems as this will answer: 16. A roof-truss lies at rest under the forces +x, +y, and −2, with arms x, y, and +8. Find the values of x and y.

The equations here needed are x+y=2, and x2-y2 = 16. Such equations will not be denied an algebraic value, even by the ultraformalist.

From now on formal problems of any of the customary algebraic types of linear, or linear and quadratic, simultaneous equations may be taken up with understanding on the pupil's part. The work will be backed up with a feeling on the part of the learner that such problems are called for by matters that have a modern meaning and a real use, at least; and this much cannot be said to the credit of the work which the high-school pupil of algebra is commonly called upon to do. High-school pupils work much better under a mixed than under a pure faith in the ultimate usefulness of what they are required to do.

Almost everyone of the foregoing equations might profitably be given a graphical treatment. It was the purpose of this paper to show at least one rich and easily accessible field to draw upon. for material to vitalize and to conceptualize the equations and functions that Mr. Moore would treat very extensively by the aid of cross-ruled paper. It is believed that enough has already been given to accomplish this purpose. If there are those who still doubt the value of such work as is here advocated, let them allow their doubts and skepticism to be dissipated by the test of practical

trial!

EARTHQUAKES IN PERU.

In 1647 within a space of two and a half months there were 120 earthquake shocks in Peru, in one of which the city of Santiago was devastated and more than a thousand persons killed.

On October 28, 1746, in the city of Lima, 10,000 persons perished from an earthquake shock, and during the 112 days following that date there were registered in Peru 400 distinct earthquake shocks.

In 1650 there were 226 shocks recorded between March 31 and May 20, in one of which the city of Cuzco was destroyed. It was of this city that a writer of that day said: "To live in this city is to die in the midst of many terrors and excitements."-The Scottish Geographical Magazine.

THE NERNST LAMP IN THE LABORATORY AND SIMPLE EXPERIMENTS ON RADIO-ACTIVITY.*

I.

By F. R. GORTON,

Michigan State Normal College, Ypsilanti, Mich.

1. The Nernst lamp consists essentially of a specially prepared filament A, Fig. 1, called the glower, and a series resistance B, called the ballast. The glower possesses the property of conducting electricity only when hot. Joining a glower and a corresponding ballast across the electric lighting mains and heating the filament in a flame brings it into a conducting condition after which the current quickly carries it to a temperature at which it gives off an intense light. The ballast consists of an iron wire of such a length and size as to offer sufficient resistance while conducting the necessary current. Obviously the glowers and the ballasts must be adapted to the voltage on which they are to operate. These parts of the lamp already described can be had neatly mounted in lamp bodies in which the initial heating of the glower is done automatically by the current. While the complete lamps are excellent for commercial lighting purposes, a more convenient mounting is desirable for use in the laboratory. One form that has been found useful for many purposes is shown in crosssection in Fig. 2. The parts are mounted on part of a porcelain

ceiling rosette used in electric wiring. BB are two brass posts passing through the screw holes in the porcelain and attaching to the small brass plates EE. The joints cannot be soldered on account of the heat produced while the lamp is in operation. To the plates EE are attached the metal extensions DD. These are drilled near the outer ends to receive the small aluminum pins with which each glower is provided. The large screw C serves to connect the lamp to the kind of holder or stand desired. The

*The cuts on ratio-activity are loaned by the Western Journal of Education.

metal parts can be protected from the intense heat of the glower by filling the holder with plaster of Paris. The electrical connections are made by attaching flexible lamp cord to the ends. of the posts BB. These contacts may be soldered. It is advisable to fit pieces of glass tubing over the posts before attaching the wires to prevent short-circuiting. The ballast may be placed anywhere in the circuit. A convenient mount is shown in Fig 3.

Fig. 3

The lamp as described serves admirably as a luminant for projection purposes for pictures five or six feet in diameter. Smaller pictures in a partially darkened room can be distinctly seen by a class. Two 110-volt glowers serve for projection in a room. seating three or four hundred.

Another application can be made in rendering galvanometer deflections visible to a class. Place the lamp about 75 cms. in front of a mirror galvanometer and a convex lens whose principal focal length is 50 cms. about 65 cms. from the lamp and between the two. A brilliant image of the glower will be reflected upon a screen or scale placed behind the lamp at a distance of about two meters. Of course, other lenses than that mentioned may be used and the correct position of all the parts found by trial. The image is bright enough to be observed without darkening the room.

A brilliant point source for experimental purposes can be produced by placing a slit near, and at right angles to, the glower. For work in optics not requiring a very narrow slit, the glower itself serves very well.

Other uses will suggest themselves to teachers of physics as they come to use this luminant. The glowers and ballasts are made both for direct and alternating currents. They can be procured from the Nernst Lamp Co., of Pittsburg, Pa., or Chicago. The nature of the current and the voltage must be stated in ordering the parts.

2. Two effects of radio-active substances are easily made use of in the laboratory; viz., the photographic action and the electrical effect due to the radiations emitted by such bodies. Probably the most accessible substance possessing the property in any

Fig. 4. Effect obtained by placing an ordinary gas mantle upon a photographic plate. The fogging of the plate shows the presence of a radioactive substance which in this case was thorium. Time of exposure, 13 days. Lighter regions produced by interposed pieces of paper.

Fig. 5. Plate exposed 13 days to the activity of the ashes of 10 gas mantles, showing presence of radio-active substance and effect of intervening pieces of paper and thin metal strip.